Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2017: 0.67

See all formats and pricing
More options …
Volume 10, Issue 5


On Courant's nodal domain theorem

Giovanni Alessandrini
Published Online: 2008-03-11 | DOI: https://doi.org/10.1515/form.10.5.521


We study the validity of Courant's nodal domain theorem for eigenfunctions of selfadjoint second order elliptic operators with low regularity assumptions on the coefficients. We prove that in two dimensions Courant's theorem holds also when the coefficients are just bounded and measurable. In the higher dimensional case, we prove a weakened version of Courant's theorem when the coefficients in the principal part are Hölder continuous.

About the article

Received: 1996-09-15

Published Online: 2008-03-11

Published in Print: 1998-09-01

Citation Information: Forum Mathematicum, Volume 10, Issue 5, Pages 521–532, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.10.5.521.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Sudhir Ranjan Jain and Rhine Samajdar
Reviews of Modern Physics, 2017, Volume 89, Number 4
John C. Urschel
Linear Algebra and its Applications, 2017
Pierre Jammes
Pacific Journal of Mathematics, 2016, Volume 282, Number 1, Page 145
Carlos Kenig, Luis Silvestre, and Jenn-Nan Wang
Communications in Partial Differential Equations, 2015, Volume 40, Number 4, Page 766
David Krejčiřík and Matěj Tušek
Journal of Differential Equations, 2015, Volume 258, Number 2, Page 281
Martin J. Gander and Felix Kwok
SIAM Review, 2012, Volume 54, Number 3, Page 573
Giovanni Alessandrini
Journal of Mathematical Analysis and Applications, 2012, Volume 386, Number 2, Page 669
Mateusz Kwaśnicki
Semigroup Forum, 2009, Volume 79, Number 1, Page 183

Comments (0)

Please log in or register to comment.
Log in